I was a large fan of both the original series, the half-release 'Death and Rebirth' and the replacement ending 'The End of Evangelion', so I'm not giving this praise as some guy who's just walked in on this.
I am extremely pleased with this new iteration of Evangelion. I don't even know where to begin ... Gainax threw out everything they had, completely redrawing all the animation and backgrounds in painstakingly high detail. It is the most apparent revision to the series at first glance ... all the visuals are top-notch, even the computer-generated graphics which I would typically find unforgivable in a film - but everything is drawn and animated so smooth, and the rare use of CG is so well-integrated into the film that it feels like you haven't been taken out of the organic animation at all.
The storyline is quite similar to the original, though first on the side I want to say they've taken much thought deciding how to develop the characters better; and the result is that the cast is much more believable and their chemistry is quite fantastic. The characters just feel deeper, their emotions are more genuine; it's hard to describe in a review but if you're a fan of the original series you'll find their personalities and interactions much more developed and satisfying.
The plot, as I've said; has not changed too much at this point.. there are exceptions here and there, with the introductions of pivotal locations and characters earlier on; no doubt to lay down continuity for the later installments. (The original Evangelion had a slight problem with eclectic character and plot point introductions.) They have taken care to set the stage more carefully for the first scene this time around; and as shown with the early introduction of an important character Gainax intends to make full use of some fantastic characters that didn't get enough time in the spotlight to really add anything especially deep.
I recommend this film to anybody who is a fan of serious animation; and I would say that it's an absolute must-see for fans of the original series.
It's comforting to know that in a world of poor remakes and extensions of popular titles, that Gainax has their wits about them and shows true dedication in their efforts to make Evangelion into everything that it could possibly be.